Redline c+ or Amsoil transmission fluid have really low cold pour points. Wait though, since you have a manual it might be d4. Any oil gets really thick when it is cold out, some base oils called pao have way better cold performance. Transmission fluid is about a 0w20 as far as viscosity, and as you can see in this chart the fluids viscosity versus temp versus weight, even thin oils are thicker then the thickest oil when warm. Sometimes just an oil change will help, but in your case I'm not sure. Look at stat sheets and pour points. But, I'm not exactly sure because you have a manual. So check the fluid level, is it low or too high? After that if you are lucky it would be in clutch, but other causes would be on hard components of trans.
Is it on oem fluid? One potential causes could be wrong fluid as well. Do you know what fluid your transmission is spec'd for?